Math ..

[Kezotar]

Exams are heading and I'm kinda struggeling with this one...

The question is in norwegian, however I'll try to translate it as good as possible...

f)

For the function "f" we've given f '(x) = a(x+1)(x-2) there the value of "a" is given by " a < 0 "..

1. Draw a it on a " http://ndla.no/sites/default/files/i...tegnslinje.png " Don't really know the english word for it..

2. Use it to decide the x value for the topp and bottom points, also decide when the graph grows and sinks.

3. Decide " f ' ' (x). Use it to decide the decide the x values for the turning point.

Sorry, I know I'm not that fluent in english and there's a couple of words I really can't get to translate...

If someone knows the answer or "advice" on how to do it, I'd appreciate it!

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Oh I am stupid.. I think it's just getting late..

I had a issue with understanding why " A's value was negative at the thing .. " But it makes sense, much sense.. Considering that A < 0 meaning that it HAS to me negative at the thing no matter what the x value is.. Jeesus, I'm stupid. Sorry to have to make a thread, can close or if someone still feel for adding a much more informative text on it and the english names for it, I'd appreciate it. !

[Dendrek]

Were you able to answer parts 1 through 3 on your own?

1) Appears to be asking you to find the two points where this function crosses the x-axis (the x-line, in your case I think that's what x-verdier is).

Do you know how to find those two points? I'll give you a hint: it's where f(x) = 0.

2) Is asking for the vertex (highest or lowest point on a parabola). One way to do that is: Find the "midpoint" between the x-intercepts (from part 1). This is the x-value of the vertex. Plug that back in to find the f(x) value. You'll get a point (x, f(x)).

To know if it's the highest or lowest point depends on if the graph is upwards facing or downwards facing. It appears you already know the answer to that question.

3) I'm really not sure what you're asking for here. Do you mean f''(x) (the second derivative)? If you're in calculus, then what I said for steps 1 and 2 might not apply to how you're supposed to solve this.

[Kezotar]

Were you able to answer parts 1 through 3 on your own?

1) Appears to be asking you to find the two points where this function crosses the x-axis (the x-line, in your case I think that's what x-verdier is).

Do you know how to find those two points? I'll give you a hint: it's where f(x) = 0.

2) Is asking for the vertex (highest or lowest point on a parabola). One way to do that is: Find the "midpoint" between the x-intercepts (from part 1). This is the x-value of the vertex. Plug that back in to find the f(x) value. You'll get a point (x, f(x)).

To know if it's the highest or lowest point depends on if the graph is upwards facing or downwards facing. It appears you already know the answer to that question.

3) I'm really not sure what you're asking for here. Do you mean f''(x) (the second derivative)? If you're in calculus, then what I said for steps 1 and 2 might not apply to how you're supposed to solve this.

http://imgur.com/Qaxa1Gr

This is what I've done.

If it actually makes sense.. However, I managed to find both of the values, and whereabout it's increasing, which basically is the part between the lower and upper.

However, now I'm being asked to

" Double Derivate ".. f '' (x) A(x+1)(x-2)

This has gotten me to something like (ax+x)(x-2) and to solve this I'm using " U' * V + U * V' "..

However why I'm not sure.. It's not that hard math.. however harder to explain

[Blueobelisk]

No a gets distributed to all the terms, not just the first the first x. (I'm assuming you meant (ax+1) and not (ax+x).)

Yes you can use the multiplication derivative rule. Might be easy to expand everything out and use the power rule, though.

[Kezotar]

No a gets distributed to all the terms, not just the first the first x. (I'm assuming you meant (ax+1) and not (ax+x).)

Yes you can either use the multiplication derivative rule. Might be easy to expand everything out and use the power rule, though.

i multiplied a into x-1 meaning a(x-1) = ax - a

[Dendrek]

Wow, I totally missed the f'(x) in the first part. lol sorry. It is Calculus. (Relooking at the problem now)

[Blueobelisk]

Oh yes that's perfect then.

[Deleted]

Guys what is wrong with you?

Math is NUMBERS.

Throwing all these shapes around. And letters! Lol, noobs. L2Math.

[Dendrek]

f '(x) = a(x+1)(x-2) there the value of "a" is given by " a < 0 "..

You don't even need to multiply the a in if you plan to use Product Rule (u'v + uv').

a[ (x+1)(x-2) ]'
a[ (x+1)'(x-2) + (x+1)(x-2)' ]
a[ (1)(x-2) + (x+1)(1) ]
a[ x-2 + x+1 ]
a[ 2x - 1 ]

[Kezotar]

You don't even need to multiply the a in if you plan to use Product Rule (u'v + uv').

a[ (x+1)(x-2) ]'
a[ (x+1)'(x-2) + (x+1)(x-2)' ]
a[ (1)(x-2) + (x+1)(1) ]
a[ x-2 + x+1 ]
a[ 2x - 1 ]

That's the answer I got to aswell, however I just can't explain to myself why we're using the product rule here.. could you explain?

[Dendrek]

That's the answer I got to aswell, however I just can't explain to myself why we're using the product rule here.. could you explain?

You first learned how to take derivatives of polynomials (a bunch of things added or subtracted, like 2x^3 + 3x^2 + x - 1, for example). When you have something more complicated, you need a way to make it easier. The Product Rule is used when you take the derivative of two "functions" that are multiplied together ("product" means "multiplication"). In this case, you have (x+1) and (x-2) multiplied together. Does that explain it better?

[Neganova]

2. Use it to decide the x value for the topp and bottom points, also decide when the graph grows and sinks.
3. Decide " f ' ' (x). Use it to decide the decide the x values for the turning point.

Too tired to do any math myself, but for those wishing to give this a go... I'm guessing "topp and bottom" mean absolute maximum and minimum points, and the graph growing and sinking is increasing and decreasing. The turning point is probably the point of inflection?

There. I've contributed!

[Kezotar]

You first learned how to take derivatives of polynomials (a bunch of things added or subtracted, like 2x^3 + 3x^2 + x - 1, for example). When you have something more complicated, you need a way to make it easier. The Product Rule is used when you take the derivative of two "functions" that are multiplied together ("product" means "multiplication"). In this case, you have (x+1) and (x-2) multiplied together. Does that explain it better?

Much better, so we're basically back the the idea when we're deravating normal things such as "6x * e^-2x" where I never in the world would be able to derevate it the same as 2x^3 + 3^2 + x -1 so we're using the product rule to make it easier. thanks alot dude, you saved me there with that!

I got one more question.. I'm kinda struggeling on the last part of the other question..

" It's finding "var(x)".

(0 - P)^2 * (1-P) + (1-P)^2 * P

I'm getting " P ( -P + 1) rather than the right answer " P ( 1-P ) or is it the same? I can't see where I'm making the mistake..

[Fexus]

I'm getting " P ( -P + 1) rather than the right answer " P ( 1-P ) or is it the same? I can't see where I'm making the mistake..

That is the same answer.

[Dendrek]

I'm getting " P ( -P + 1) rather than the right answer " P ( 1-P ) or is it the same? I can't see where I'm making the mistake..

Those are the same. Think of it this way:

When you are adding numbers, it doesn't matter what order you add them in. For example, 2 + 5 is the same as 5 + 2. It's called the Commutative Property of Addition. This is true even if one of those numbers is negative. So -3 + 8 is the same as 8 + -3. And 8 + -3 is the same as 8 - 3.

In your case, -P + 1 is the same as 1 + -P, which is also 1 - P.

[Kezotar]

That is the same answer.

Oh it is? That's a relief, means that I've spent 30 minutes figuring why I am wrong was that I was right. Haha. Good.

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Those are the same. Think of it this way:

When you are adding numbers, it doesn't matter what order you add them in. For example, 2 + 5 is the same as 5 + 2. It's called the Commutative Property of Addition. This is true even if one of those numbers is negative. So -3 + 8 is the same as 8 + -3. And 8 + -3 is the same as 8 - 3.

In your case, -P + 1 is the same as 1 + -P, which is also 1 - P.

So for a exam what would be the prefered way? I mean is it just a order which absolutely has no meaning? If yeah, I'm over that one. Haha.. 05:03 and still studying, lection in 7 hours, gogo. haha


Thanks alot to you guys that helped me, you really did a great job!

[Dendrek]

So for a exam what would be the prefered way? I mean is it just a order which absolutely has no meaning? If yeah, I'm over that one. Haha.. 05:03 and still studying, lection in 7 hours, gogo. haha

Either is ok. 1 - P looks better, but you'd get full credit for -P + 1. It is important that you recognized they are both the same, though.

[Fexus]

Oh it is? That's a relief, means that I've spent 30 minutes figuring why I am wrong was that I was right. Haha. Good.

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So for a exam what would be the prefered way? I mean is it just a order which absolutely has no meaning? If yeah, I'm over that one. Haha.. 05:03 and still studying, lection in 7 hours, gogo. haha

The order doesn't matter mathematically; however, I assume by var(x) you are referring to variance and P is a probability. (1 - P) I would argue is a better way to visualize the concept. It is completely preference.

[Kezotar]

Either is ok. 1 - P looks better, but you'd get full credit for -P + 1. It is important that you recognized they are both the same, though.

It makes sense, but I just couldn't be 100% sure..

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The order doesn't matter mathematically; however, I assume by var(x) you are referring to variance and P is a probability. (1 - P) I would argue is a better way to visualize the concept. It is completely preference.

Yeah, you're correct. That's good to know, I'll stick with what looks best. Much thanks to you Dendrek and Fexus !! Is it okey if I ask you guys for a couple more things, not right now but maybe later?

[Fexus]

It makes sense, but I just couldn't be 100% sure..

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Yeah, you're correct. That's good to know, I'll stick with what looks best. Much thanks to you Dendrek and Fexus !! Is it okey if I ask you guys for a couple more things, not right now but maybe later?

Not a problem. I should be checking gen OT periodically for the next hour or two.